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New Greedy-Like Heuristics for the Multidimensional 0-1 Knapsack Problem

Richard Loulou, Eleftherios Michaelides

Open publisher page 113 citations

Abstract

In this paper, we develop four heuristic methods to obtain approximate solutions to the multidimensional 0-1 knapsack problem. The four methods are tested on a number of problems of various sizes. The solutions are compared to the rigorous optimum as well as to a heuristic method of Toyoda. They are statistically better than the latter, with average relative errors of the order of less than 1%.

About this research paper

What this paper is about

In this paper, we develop four heuristic methods to obtain approximate solutions to the multidimensional 0-1 knapsack problem. The four methods are tested on a number of problems of various sizes. The solutions are compared to the rigorous optimum as well as to a heuristic method of Toyoda. They are statistically better than the latter, with average relative errors of the order of less than 1%.

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OpenAlex reports 113 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In this paper, we develop four heuristic methods to obtain approximate solutions to the multidimensional 0-1 knapsack problem. The four methods are tested on a number of problems of various sizes. The solutions are compared to the rigorous optimum as well as to a heuristic method of Toyoda. They are statistically better than the latter, with average relative errors of the order of less than 1%.

Key concepts: Knapsack problem, Continuous knapsack problem, Heuristics, Greedy algorithm, Mathematical optimization, Heuristic, Change-making problem, Order (exchange)

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